# NCERT solutions for Class 10 Maths chapter 2 - Polynomials [Latest edition]

#### Chapters ## Chapter 2: Polynomials

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4
Exercise 2.1 [Page 28]

### NCERT solutions for Class 10 Maths Chapter 2 PolynomialsExercise 2.1 [Page 28]

Exercise 2.1 | Q 1.1 | Page 28

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in the following. Exercise 2.1 | Q 1.2 | Page 28

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x) Exercise 2.1 | Q 1.3 | Page 28

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x) Exercise 2.1 | Q 1.4 | Page 28

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x) Exercise 2.1 | Q 1.5 | Page 28

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x) Exercise 2.1 | Q 1.6 | Page 28

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x) Exercise 2.2 [Page 33]

### NCERT solutions for Class 10 Maths Chapter 2 PolynomialsExercise 2.2 [Page 33]

Exercise 2.2 | Q 1.1 | Page 33

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

x2 – 2x – 8

Exercise 2.2 | Q 1.2 | Page 33

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

4s2 – 4s + 1

Exercise 2.2 | Q 1.3 | Page 33

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

6x2 – 3 – 7x

Exercise 2.2 | Q 1.4 | Page 33

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

4u2 + 8u

Exercise 2.2 | Q 1.5 | Page 33

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

t2 – 15

Exercise 2.2 | Q 1.6 | Page 33

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

3x2 – x – 4

Exercise 2.2 | Q 2.1 | Page 33

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

1/4 , -1

Exercise 2.2 | Q 2.2 | Page 33

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

sqrt2 , 1/3

Exercise 2.2 | Q 2.3 | Page 33

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

0, sqrt5

Exercise 2.2 | Q 2.4 | Page 33

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

1, 1

Exercise 2.2 | Q 2.5 | Page 33

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

-1/4 ,1/4

Exercise 2.2 | Q 2.6 | Page 33

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

4, 1

Exercise 2.3 [Page 36]

### NCERT solutions for Class 10 Maths Chapter 2 PolynomialsExercise 2.3 [Page 36]

Exercise 2.3 | Q 1.1 | Page 36

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following

p(x) = x3 – 3x2 + 5x – 3, g(x) = x2 – 2

Exercise 2.3 | Q 1.2 | Page 36

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : p(x) = x4 – 3x2 + 4x + 5,   g(x) = x2 + 1 – x

Exercise 2.3 | Q 1.3 | Page 36

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following

p(x) = x4 – 5x + 6, g(x) = 2 – x2

Exercise 2.3 | Q 2.1 | Page 36

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial

t2 – 3, 2t4 + 3t3 – 2t2 – 9t – 12

Exercise 2.3 | Q 2.2 | Page 36

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial

x2 + 3x + 1, 3x4 + 5x3 – 7x2 + 2x + 2

Exercise 2.3 | Q 2.3 | Page 36

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial

x3 – 3x + 1, x5 – 4x3 + x2 + 3x + 1

Exercise 2.3 | Q 3 | Page 36

Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are sqrt(5/3) and - sqrt(5/3)

Exercise 2.3 | Q 4 | Page 36

On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x)

Exercise 2.3 | Q 5.1 | Page 36

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg p(x) = deg q(x)

Exercise 2.3 | Q 5.2 | Page 36

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg q(x) = deg r(x)

Exercise 2.3 | Q 5.3 | Page 36

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg r(x) = 0

Exercise 2.4 [Pages 36 - 37]

### NCERT solutions for Class 10 Maths Chapter 2 PolynomialsExercise 2.4 [Pages 36 - 37]

Exercise 2.4 | Q 1.1 | Page 36

Verify that the numbers given along side of the cubic polynomials are their zeroes. Also verify the relationship between the zeroes and the coefficients.

2x^3 + x^2 – 5x + 2 ; 1/2, 1, – 2

Exercise 2.4 | Q 1.2 | Page 36

Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case

x3 – 4x2 + 5x – 2; 2, 1, 1

Exercise 2.4 | Q 2 | Page 36

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively

Exercise 2.4 | Q 3 | Page 37

If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b

Exercise 2.4 | Q 4 | Page 37

If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± sqrt3 , find other zeroes

Exercise 2.4 | Q 5 | Page 37

If the polynomial x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k, the remainder comes out to be x + a, find k and a.

## Chapter 2: Polynomials

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4 ## NCERT solutions for Class 10 Maths chapter 2 - Polynomials

NCERT solutions for Class 10 Maths chapter 2 (Polynomials) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 10 Maths solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10 Maths chapter 2 Polynomials are Geometrical Meaning of the Zeroes of a Polynomial, Relationship Between Zeroes and Coefficients of a Polynomial, Division Algorithm for Polynomials, Concept of Polynomials, Concept of Polynomials, Geometrical Meaning of the Zeroes of a Polynomial, Relationship Between Zeroes and Coefficients of a Polynomial, Division Algorithm for Polynomials, Concept of Polynomials, Concept of Polynomials.

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